Intermediate valence of Ce in Ce1−xScxPd3

We present the lattice constant and susceptibility data of Ce_1?xSc_xPd₃ and report on the ESR in (Ce_1?xSc_x0.995Gd_0.005Pd₃. A transition from tetravalent cerium for x ? 0.5 to an intermediate valent state for x ? 0.3 is clearly shown by all three measuring methods.     

Conical diffraction by periodic structures: Variation of interfaces and gradient formulas

This paper studies the dependence of solutions to conical diffraction problems upon geometric parameters of non–smooth profiles and interfaces between different materials of diffractive gratings. This problem arises in the design of those optical devices to diffract time–harmonic oblique incident plane waves to a specified far–field pattern. We prove the stability of solutions and give analytic formulas for the derivatives of reflection and transmission coefficients with respect to Lipschitz perturbations of interfaces. These derivatives are expressible as contour integrals involving the direct and adjoint solutions of conical diffraction problems.     

The collocation method for mixed boundary value problems on domains with curved polygonal boundaries

Summary. We consider an indirect boundary integral equation formulation for the mixed Dirichlet-Neumann boundary value problem for the Laplace equation on a plane domain with a polygonal boundary. The resulting system of integral equations is solved by a collocation method which uses a mesh grading transformation and a cosine approximating space. The mesh grading transformation method yields fast convergence of the collocation solution by smoothing the singularities of the exact solution. A complete stability and solvability analysis of the transformed integral equations is given by use of a Mellin transform technique, in a setting in which each arc of the polygon has associated with it a periodic Sobolev space. Received April 15, 1995 / Revised version received April 10, 1996     

On Spline Approximation for Singular Integral Equations on an Interval

This paper analyses the convergence of spline approximation methods for strongly elliptic singular integral equations on a finite interval. We consider collocation by smooth polynomial splines of odd degree multiplied by a weight function and a Galerkin-Petrov method with spline trial functions of even degree and piecewise constant test functions. We prove the stability of the methods in weighted Sobolev spaces and obtain the optimal orders of convergence in the case of graded meshes.     

Characterization of hydrothermally isolated xylan from beech wood by capillary electrophoresis with laser-induced fluorescence and mass spectrometry detection

Hemicelluloses such as xylans play an increasing role as renewable raw materials for technological applications. The complex and variable composition of hemicelluloses requires powerful analytical techniques in order to assess their composition. In the present study, the neutral fraction of hydrothermally isolated xylan from beech wood was characterized by capillary electrophoresis with laser-induced fluorescence detection (CE-LIF) upon derivatization with 8-aminopyrene-1,3,6-trisulfonic acid. Reproducible separation of the xylo-oligosaccharides was achieved using a polyvinyl alcohol coated capillary and a 25 mM sodium acetate buffer, pH 4.75, as background electrolyte at an applied voltage of ?30 kV. Intermediate precision expressed as relative standard deviation was below 2.0 % for migration times and below 10 % for relative peak areas except for the oligomers present at very low concentrations only. At the same time, derivatization conditions proved to be robust as well. Samples obtained by fractionation of the xylan were subsequently characterized by CE-LIF. In addition, capillary electrophoresis with mass spectrometry detection indicated the presence of small amounts of xylo-oligosaccharides containing additional sugar moieties such as 4-O-methylglucuronic acid. Moreover, minor components containing acetyl groups could be detected. The presence of these impurities was confirmed by nuclear magnetic resonance analysis of the fractions. In conclusion, although none of the techniques applied here gave a complete picture of the composition of the investigated xylan or its fractions, the combination provided insight into the complexity of the sample.     

Galerkin methods with splines for singular integral equations over (0, 1)

Summary In this paper a convergence analysis of Galerkin methods with splines for strongly elliptic singular integral equations over the interval (0, 1) is given. As trial functions we utilize smoothest polynomial splines on arbitrary meshes and continuous splines on special nonuniform partitions, multiplied by a weight function. Using inequalities of Gårding type for singular integral operators in weightedL ² spaces and the complete asymptotics of solutions at the endpoints, we provide error estimates in certain Sobolev norms.